A fully distributed mathematical model, describing the performance of a single porous compounded bifunctional catalyst pellet, promoting complex endothermic reforming reactions, demonstrates that isothermal conditions obtain within the catalyst pellet. The heat transfer resistance, therefore, resides entirely within the fluid film surrounding the catalyst particle. Application of such a lumped thermal resistance model is then extended to the examination of systems involving a physical mixture of discrete catalyst pellets. Steady state stability analyses of both bifunctional catalyst systems show that, in the case of discrete pellet mixtures contained in a reactor operated in a high temperature region, alternative stationary states may exist because one of the two types of particle supports overall exothermic reactions. A one-dimensional steady state reactor model is employed to predict the behaviour of reactors packed with the two different bifunctional catalyst preparations and which promote chemical reaction in the presence of mass and heat transfer effects. It is concluded that a compounded bifunctional catalyst is, in practice, superior to a physical mixture of discrete pellets due to the favourable mass and heat transfer characteristics of such a catalyst. It is also demonstrated that the complex reactions occurring over compounded pellets may be reasonably described by a relatively simple reaction scheme which emphasizes the role of a cooperative reaction step effecting direct conversion of methyl cyclo-pentene to benzene. Consequently, the overall complexity of the mathematical model and the high computational effort are reduced considerably. Optimisation of benzene yield with respect to the bifunctional catalyst composition indicates that it is more economic, in practice, to employ an optimum uniform catalyst composition than a spatially distributed optimum (e.g. a falling profile along the reactor) since the former policy gives a product yield which is only very slightly lower than for the latter case. A simplified unsteady state mathematical model of a reforming reactor packed with compounded pellets shows that the reactor is stable, for a wide range of operating conditions, when subjected to step perturbations in inlet fluid conditions. However, the approach to the new steady state is found to be particularly slow in the case of adiabatic operation. This is most likely due to the low overall chemical reaction rate. A well known initial value (i.e. stepwise) numerical technique is shown to be suitable for integration of the state equations, both spatially along the reactor and in the time domain, provided that an appropriate arithmetic precision is employed. Furthermore, the computational effort is reduced considerably by using a suitable integration step size distribution in the time domain.
|Date of Award||1975|